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Resilient Dynamic Programming

2015
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Algorithmica
*

We investigate the design of dynamic programming algorithms in unreliable memories, i.e., in the presence of errors that lead the logical state of some bits to be read differently from how they were last written. Assuming that a limited number of memory faults can be inserted at run-time by an adversary with unbounded computational power, we obtain the first resilient algorithms for a broad range of dynamic programming problems, devising a general framework that can be applied to both iterative

doi:10.1007/s00453-015-0073-z
fatcat:c6lzvh2ahnd4lfulgxseys6qha
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... and recursive implementations. Besides all local dependency problems, where updates to table entries are determined by the contents of neighboring cells, we also settle challenging non-local problems, such as all-pairs shortest paths and matrix multiplication. All our algorithms are correct with high probability and match the running time of their standard non-resilient counterparts while tolerating a polynomial number of faults. The recursive algorithms are also cacheefficient and can tolerate faults at any level of the memory hierarchy. Our results exploit a careful combination of data replication, majority techniques, fingerprint computations, and lazy fault detection. To cope with the complex data access patterns induced by some of our algorithms, we also devise amplified fingerprints, which might be of independent interest in the design of resilient algorithms for different problems.##
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Knowledge, Level of Symmetry, and Time of Leader Election
[article]

2015
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arXiv
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pre-print

Figure 5 5 : a) Graph

arXiv:1508.01300v1
fatcat:guoo2yyyjvcjxmn77rbsx5xvri
*G*2 . b) Graph*G*2 . ... Let*G*be any graph in class C. If leader election is possible for the graph*G*, then it is accomplished. • Strong LE. Let*G*be any graph in class C. ...##
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Topology recognition with advice

2016
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Information and Computation
*

,

doi:10.1016/j.ic.2016.01.005
fatcat:kh6ret3h3vfpvleix3ojh66l7i
*G*1 or*G*2*G*2 ,*G*1 , or*G*2 . ... Figure 1 : a) Graphs*G*1 and*G*2 from [31] . b) Graphs*G*1 and*G*2 . c) Schematic representation of graphs H 1 and H 2 , in which the rectangle represents one of the graphs*G*1 , (b)*G*2 (c)*G*1 ,*G*2 ...##
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Distributed tree comparison with nodes of limited memory

2012
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Networks
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. , k−1, let |

doi:10.1002/net.21463
fatcat:3xwuhphpvrfnbm6ohofennixlm
*g*i (σ)| denote the number of messages in*g*i (σ). ... . , k − 1, there is a subset of at least 2 j+1 instances σ, such that |*g*i (σ)| ≥ j/x. ... . , k − 1 and any distinct instances σ, σ from Σ, we have*g*i (σ) =*g*i (σ ). ...##
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Learning a Ring Cheaply and Fast
[chapter]

2013
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Lecture Notes in Computer Science
*

By the definition of communication delay induced on a path, we have

doi:10.1007/978-3-642-39212-2_49
fatcat:4qdyntjb3veqdkdx2ea4oph2fe
*g*({x h+p , x h+p+1 }, r p ) = 1, for all 0 ≤ p < D. We now show that sets Z y are pairwise disjoint. ... Elements of Z y are ordered pairs composed of an edge and a round number, of the form ({x h+p , x h+p+1 }, r p ), for 0 ≤ p < D, where r p = δ( x h . . . x h+p+1 ,*g*) + p + 1. ...##
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How much memory is needed for leader election

2011
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Distributed computing
*

Let

doi:10.1007/s00446-011-0131-y
fatcat:uraxymdl6rfyvjwgm7bwxiuefa
*G*be any graph in class C. If leader election is possible for the graph*G*, then LE is accomplished. • Strong LE. Let*G*be any graph in class C. ... If leader election is possible for the graph*G*, then LE is accomplished. ...##
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Acknowledged broadcasting in ad hoc radio networks

2008
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Information Processing Letters
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We consider ad hoc radio networks in which each node knows only its own identity but is unaware of the topology of the network, or of any bound on its size or diameter. Acknowledged broadcasting (AB) is a communication task consisting in transmitting a message from a distinguished source to all other nodes of the network and making this fact common knowledge among all nodes. To do this, the underlying directed graph must be strongly connected. Working in a model allowing all nodes to transmit

doi:10.1016/j.ipl.2008.09.011
fatcat:udzaqc7vjje2fphof2i46zgrci
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... ontaneously even before getting the source message, Chlebus et al. [6] proved that AB is impossible, if collision detection is not available, and gave an AB algorithm using collision detection that works in time O(nD) where n is the number of nodes and D is the eccentricity of the source. Uchida et al. [29] showed an AB algorithm without collision detection working in time O(n 4/3 log 10/3 n) for all strongly connected networks of size at least 2. In particular, it follows that the impossibility result from [6] is really caused by the singleton network for which AB amounts to realize that the source is alone. We improve those two results by presenting two generic AB algorithms using a broadcasting algorithm without acknowledgement, as a procedure. For a large class of broadcasting algorithms the resulting AB algorithm has the same time complexity. Using the currently best known broadcasting algorithms, we obtain an AB algorithm with collision detection working in time O(min{n log 2 D, n log n log log n}), for arbitrary strongly connected networks, and an AB algorithm without collision detection working in time O(n log n log log n) for all strongly connected networks of size n ≥ 2. Moreover, we show that in the model in which only nodes that already got the source message can transmit, AB is infeasible in a strong sense: for any AB algorithm there exists an infinite family of networks for which this algorithm is incorrect.##
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Knowledge, level of symmetry, and time of leader election

2014
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Distributed computing
*

Let

doi:10.1007/s00446-014-0237-0
fatcat:l653tdifujdx5ob5opus24j5x4
*G*be any graph in class C. If leader election is possible for the graph*G*, then it is accomplished. -Strong leader election. Let*G*be any graph in class C. ... Let*G*be a graph. The following conditions are equivalent: 1. Leader election is possible in*G*; 2. Views of all nodes are different; 3. There exists a node with a unique view. ...##
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How Much Memory Is Needed for Leader Election
[chapter]

2010
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Lecture Notes in Computer Science
*

Let

doi:10.1007/978-3-642-15763-9_25
fatcat:xrhi247zfreuxd4nr4qusm72fy
*G*be any graph in class C. If leader election is possible for the graph*G*, then LE is accomplished. • Strong LE. Let*G*be any graph in class C. ... If leader election is possible for the graph*G*, then LE is accomplished. ...##
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Broadcasting in UDG radio networks with missing and inaccurate information

2010
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Distributed computing
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They proved that the minimum broadcasting time is Θ'min˘D +

doi:10.1007/s00446-010-0093-5
fatcat:uazll5wrvrgw7lyfj66dyljjum
*g*2 , D log*g*¯´, assuming that each node knows the density of the network and knows exactly its own position in the plane. ... Nevertheless, under our very weak scenario, we construct a broadcasting algorithm that maintains optimal time O'min˘D +*g*2 , D log*g*¯´for all networks with at least 2 nodes, of diameter D and granularity ... (*g*2 ). ...##
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Knowledge, Level of Symmetry, and Time of Leader Election
[chapter]

2012
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Lecture Notes in Computer Science
*

Let

doi:10.1007/978-3-642-33090-2_42
fatcat:nxp4kutxp5gx7ngkkh3ov7sltm
*G*be any graph in class C. If leader election is possible for the graph*G*, then it is accomplished. -Strong leader election. Let*G*be any graph in class C. ... Let*G*be a graph. The following conditions are equivalent: 1. Leader election is possible in*G*; 2. Views of all nodes are different; 3. There exists a node with a unique view. ...##
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Communication Complexity of Consensus in Anonymous Message Passing Systems
[chapter]

2011
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Lecture Notes in Computer Science
*

Let

doi:10.1007/978-3-642-25873-2_14
fatcat:iycm4mrwpba7hcbq4pgsuwvoyy
*G*be a fully symmetric connected n-node graph. Then there exists a fully symmetric connected spanning subgraph*G*of*G*with at most n log n edges. ... visit of*G*starting from u to the node having the same number in the breadth-first visit of*G*starting from v. ...##
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Trade-offs Between the Size of Advice and Broadcasting Time in Trees

2009
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Algorithmica
*

We study the problem of the amount of information required to perform fast broadcasting in tree networks. The source located at the root of a tree has to disseminate a message to all nodes. In each round each informed node can transmit to one child. Nodes do not know the topology of the tree but an oracle knowing it can give a string of bits of advice to the source which can then pass it down the tree with the source message. The quality of a broadcasting algorithm with advice is measured by

doi:10.1007/s00453-009-9361-9
fatcat:skjwaw4nd5fuxm443ovruhfnfu
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... competitive ratio: the worst case ratio, taken over n-node trees, between the time of this algorithm and the optimal broadcasting time in the given tree. Our goal is to find a trade-off between the size of advice and the best competitive ratio of a broadcasting algorithm for n-node trees. We establish such a trade-off with an approximation factor of O(n ), for an arbitrarily small positive constant . This is the first problem for which a trade-off between the amount of provided information and the efficiency of the solution is shown for arbitrary size of advice.##
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L(h,1,1)-Labeling of Outerplanar Graphs
[chapter]

2006
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Lecture Notes in Computer Science
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Any OBFT(

doi:10.1007/11780823_21
fatcat:qyqwubzahnf2hgao5rkvumqn5a
*G*) of an outerplanar graph*G*is an outerplanar embedding of*G*. Proof. ... Let*G*be an outerplanar graph with its associated OBFT(*G*), and two siblings x and y, x < y, in OBFT(*G*). ...##
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Impact of Information on the Complexity of Asynchronous Radio Broadcasting
[chapter]

2008
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Lecture Notes in Computer Science
*

(

doi:10.1007/978-3-540-92221-6_21
fatcat:wbsq54nxhfcjtpm62akmvcp5ti
*g*= 1/d); c, α and β are constants. ... In this case, in the formulae for the upper and lower bounds on the work, the parameter*g*= 1/d should be replaced by*g*= 1/d . ...
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